I'm building software which solves an edge case that hasn't been accounted for in the industry I'm targeting.
Potential customers I've interviewed have expressed interest and willingness to pay for the solution, but some have actually requested that instead of turning it into a product, I should instead licence it to one of the big industry players so it can be properly integrated into one of the industry's standard applications.
Could anyone offer advice / thoughts / experiences on licensing or selling software to a large entity?
The large entity would be your only customer. It would control sales and dictate your income. The organization making the suggestion is not a potential customer. That's ok. It just means that the edge case is not very important to that organization.